Equivalent in LaTeX (\equiv)

Where it is used

Triple-bar relation meaning identically equal, congruent modulo n, or logically equivalent.

Number theory writes a \equiv b \pmod{n} for congruence, analysis writes f \equiv 0 to say a function vanishes everywhere, and logic uses it for logical equivalence of formulas. Pair it with \pmod{n} for the parenthesized modulus or \bmod for the binary form a \bmod n. It is distinct from \cong (isomorphism or geometric congruence) and from \triangleq or := (definitions), although some authors also use it for definitions. Negate it with \not\equiv. In physics, \equiv often introduces a shorthand: \omega \equiv 2\pi f.

Also listed under: Logic & Proofs, Number Theory, Computer Science

Minimal compilable example

Paste this into an empty .tex file and compile it with pdfLaTeX, XeLaTeX or LuaLaTeX.

\documentclass{article}
\begin{document}
Equivalent: $\equiv$

\[ a^{p-1} \equiv 1 \pmod{p} \]
\end{document}

Related symbols

• Proportional To\propto
• Approximately Equal\approx
• Similar To\sim
• Not Equal\neq
• Congruent\cong
• Greater Than or Equal\geq

Frequently asked questions

How do I write Equivalent in LaTeX?

Type \equiv in math mode, for example $a^{p-1} \equiv 1 \pmod{p}$. It works in plain LaTeX without loading any package.

Which package do I need for \equiv?

None. \equiv is part of standard LaTeX, so it compiles with nothing in the preamble but the document class.

Can I use \equiv in text mode, or only in math mode?

Only in math mode. Outside $...$ LaTeX stops with "Missing $ inserted", so write $\equiv$ in running text. If you only need the glyph in text, paste the Unicode character ≡ instead (with XeLaTeX or LuaLaTeX and a font that has it).